Basic properties
| Modulus: | \(1375\) | |
| Conductor: | \(1375\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(100\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1375.cn
\(\chi_{1375}(87,\cdot)\) \(\chi_{1375}(98,\cdot)\) \(\chi_{1375}(142,\cdot)\) \(\chi_{1375}(153,\cdot)\) \(\chi_{1375}(197,\cdot)\) \(\chi_{1375}(208,\cdot)\) \(\chi_{1375}(252,\cdot)\) \(\chi_{1375}(263,\cdot)\) \(\chi_{1375}(362,\cdot)\) \(\chi_{1375}(373,\cdot)\) \(\chi_{1375}(417,\cdot)\) \(\chi_{1375}(428,\cdot)\) \(\chi_{1375}(472,\cdot)\) \(\chi_{1375}(483,\cdot)\) \(\chi_{1375}(527,\cdot)\) \(\chi_{1375}(538,\cdot)\) \(\chi_{1375}(637,\cdot)\) \(\chi_{1375}(648,\cdot)\) \(\chi_{1375}(692,\cdot)\) \(\chi_{1375}(703,\cdot)\) \(\chi_{1375}(747,\cdot)\) \(\chi_{1375}(758,\cdot)\) \(\chi_{1375}(802,\cdot)\) \(\chi_{1375}(813,\cdot)\) \(\chi_{1375}(912,\cdot)\) \(\chi_{1375}(923,\cdot)\) \(\chi_{1375}(967,\cdot)\) \(\chi_{1375}(978,\cdot)\) \(\chi_{1375}(1022,\cdot)\) \(\chi_{1375}(1033,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{100})$ |
| Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\((1002,376)\) → \((e\left(\frac{77}{100}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 1375 }(1022, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{100}\right)\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{27}{50}\right)\) | \(e\left(\frac{33}{50}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{81}{100}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{93}{100}\right)\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{11}{50}\right)\) |